SOLUTION: Please help me with this Max and Min question Find the absolute maximum and absolute minimum values of f on the given interval. (Round your answers to two decimal places.) f(x) =

Algebra ->  Functions -> SOLUTION: Please help me with this Max and Min question Find the absolute maximum and absolute minimum values of f on the given interval. (Round your answers to two decimal places.) f(x) =      Log On


   

Question 1155991: Please help me with this Max and Min question
Find the absolute maximum and absolute minimum values of f on the given interval. (Round your answers to two decimal places.)
f(x) = ln(x^2 + x + 2)
[-1, 1]
Answer by greenestamps(13200) About Me  (Show Source):
You can put this solution on YOUR website!


ln(x) is a monotonically increasing function: if A > B then ln(A) > ln(B), and vice versa.

So ln%28x%5E2%2Bx%2B2%29 will have its minimum value when x%5E2%2Bx%2B2%29 has its minimum value. You can find the minimum value of ln%28x%5E2%2Bx%2B2%29 using your knowledge of quadratic functions.

For the maximum value of ln%28x%5E2%2Bx%2B2%29, simply evaluate it at the two given endpoints and see which is greater.

Note also that, again since ln(x) is monotonic increasing, you can tell which endpoint gives the maximum value of ln%28x%5E2%2Bx%2B2%29 by finding on which endpoint the value of x%5E2%2Bx%2B2 is greater.